Exercise , Chapter 12
setwd("/Users/Nashrah/Desktop/Columbia_QMSS/Spring 2018 Courses/Advanced Regression Modeling")
df <- read.delim2("NES.txt", header = TRUE, sep = " ", dec = ".")
write.table(df, file="NES.dat", row.names=TRUE)
NES <- read.table("NES.dat", header = TRUE)
NES_sub <- NES$year==1992 & !is.na(NES$rvote) & !is.na(NES$dvote) & (NES$rvote==1 | NES$dvote==1)
NES92 <- NES[NES_sub,]
# logistic regression of vote preference on income
fit_1 <- glm(rvote ~ income, family=binomial(link="logit"), data=NES92)
display(fit_1)
## glm(formula = rvote ~ income, family = binomial(link = "logit"),
## data = NES92)
## coef.est coef.se
## (Intercept) -1.40 0.19
## income 0.33 0.06
## ---
## n = 1179, k = 2
## residual deviance = 1556.9, null deviance = 1591.2 (difference = 34.3)
stan_fit_1 <- stan_glm(rvote ~ income, family=binomial(link="logit"), data=NES92)
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print(stan_fit_1)
## stan_glm
## family: binomial [logit]
## formula: rvote ~ income
## observations: 1179
## predictors: 2
## ------
## Median MAD_SD
## (Intercept) -1.4 0.2
## income 0.3 0.1
##
## Sample avg. posterior predictive distribution of y:
## Median MAD_SD
## mean_PPD 0.4 0.0
##
## ------
## For info on the priors used see help('prior_summary.stanreg').
fit_2 <- glm(rvote ~ income + educ2 + str_partyid, family=binomial(link="logit"), data=NES92)
display(fit_2)
## glm(formula = rvote ~ income + educ2 + str_partyid, family = binomial(link = "logit"),
## data = NES92)
## coef.est coef.se
## (Intercept) -1.52 0.30
## income 0.28 0.06
## educ2 0.07 0.04
## str_partyid -0.02 0.06
## ---
## n = 1178, k = 4
## residual deviance = 1552.8, null deviance = 1590.2 (difference = 37.4)
stan_fit_2 <- stan_glm(rvote ~ income + educ2 + str_partyid, family=binomial(link="logit"), data=NES92)
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print(stan_fit_2)
## stan_glm
## family: binomial [logit]
## formula: rvote ~ income + educ2 + str_partyid
## observations: 1178
## predictors: 4
## ------
## Median MAD_SD
## (Intercept) -1.5 0.3
## income 0.3 0.1
## educ2 0.1 0.0
## str_partyid 0.0 0.1
##
## Sample avg. posterior predictive distribution of y:
## Median MAD_SD
## mean_PPD 0.4 0.0
##
## ------
## For info on the priors used see help('prior_summary.stanreg').
fit_3 <- glm(rvote ~ income + educ2 + black + female + str_partyid, family=binomial(link="logit"), data=NES92)
display(fit_3)
## glm(formula = rvote ~ income + educ2 + black + female + str_partyid,
## family = binomial(link = "logit"), data = NES92)
## coef.est coef.se
## (Intercept) -1.26 0.32
## income 0.23 0.07
## educ2 0.06 0.04
## black -2.68 0.37
## female -0.08 0.13
## str_partyid 0.04 0.07
## ---
## n = 1178, k = 6
## residual deviance = 1446.2, null deviance = 1590.2 (difference = 144.0)
stan_fit_3 <- stan_glm(rvote ~ income + educ2 + black + female + str_partyid, family=binomial(link="logit"), data=NES92)
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print(stan_fit_3)
## stan_glm
## family: binomial [logit]
## formula: rvote ~ income + educ2 + black + female + str_partyid
## observations: 1178
## predictors: 6
## ------
## Median MAD_SD
## (Intercept) -1.3 0.3
## income 0.2 0.1
## educ2 0.1 0.0
## black -2.7 0.4
## female -0.1 0.1
## str_partyid 0.0 0.1
##
## Sample avg. posterior predictive distribution of y:
## Median MAD_SD
## mean_PPD 0.4 0.0
##
## ------
## For info on the priors used see help('prior_summary.stanreg').
fit_4 <- glm(rvote ~ income + educ2 + black + female + ideo + str_partyid, family=binomial(link="logit"), data=NES92)
display(fit_4)
## glm(formula = rvote ~ income + educ2 + black + female + ideo +
## str_partyid, family = binomial(link = "logit"), data = NES92)
## coef.est coef.se
## (Intercept) -4.08 0.44
## income 0.10 0.08
## educ2 0.24 0.05
## black -2.69 0.39
## female 0.15 0.15
## ideo 0.71 0.05
## str_partyid -0.01 0.08
## ---
## n = 1133, k = 7
## residual deviance = 1082.1, null deviance = 1534.1 (difference = 452.0)
stan_fit_4 <- stan_glm(rvote ~ income + educ2 + black + female + ideo + str_partyid, family=binomial(link="logit"), data=NES92)
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print(stan_fit_4)
## stan_glm
## family: binomial [logit]
## formula: rvote ~ income + educ2 + black + female + ideo + str_partyid
## observations: 1133
## predictors: 7
## ------
## Median MAD_SD
## (Intercept) -4.1 0.5
## income 0.1 0.1
## educ2 0.2 0.1
## black -2.7 0.4
## female 0.2 0.2
## ideo 0.7 0.0
## str_partyid 0.0 0.1
##
## Sample avg. posterior predictive distribution of y:
## Median MAD_SD
## mean_PPD 0.4 0.0
##
## ------
## For info on the priors used see help('prior_summary.stanreg').
#selected model:
fit_4 <- glm(rvote ~ income + educ2 + income:educ2 + black + female, family=binomial(link="logit"), data=NES92)
display(fit_4)
## glm(formula = rvote ~ income + educ2 + income:educ2 + black +
## female, family = binomial(link = "logit"), data = NES92)
## coef.est coef.se
## (Intercept) -1.15 0.49
## income 0.24 0.17
## educ2 0.07 0.12
## black -2.67 0.37
## female -0.09 0.13
## income:educ2 0.00 0.04
## ---
## n = 1179, k = 6
## residual deviance = 1447.9, null deviance = 1591.2 (difference = 143.3)
stan_fit_4 <- stan_glm(rvote ~ income + educ2 + income:educ2 + black + female, family=binomial(link="logit"), data=NES92)
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print(stan_fit_4)
## stan_glm
## family: binomial [logit]
## formula: rvote ~ income + educ2 + income:educ2 + black + female
## observations: 1179
## predictors: 6
## ------
## Median MAD_SD
## (Intercept) -1.2 0.5
## income 0.2 0.2
## educ2 0.1 0.1
## black -2.7 0.4
## female -0.1 0.1
## income:educ2 0.0 0.0
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## Sample avg. posterior predictive distribution of y:
## Median MAD_SD
## mean_PPD 0.4 0.0
##
## ------
## For info on the priors used see help('prior_summary.stanreg').
#the textbook recommends using the following tricks to best interpret the results:
#1)evaluate predictions from the mean of variables and to divide by 4 to get approximate predictive differences on the prob scale
#intercept: logit^-1(-1.15+.24*3.1+0.07*4.3-2.67*0.133-0.09*0.533+0*3.1*4.3) = ~ -0.5
#income: 3.1
#education: 4.3
#black: 0.133
#female: 0.553
#having a little bit of a hard time understanding how to implement these steps for the above regression
